Question

A skilled chess player believes that when they play a novice opponent, there is a 90% probability they will be able to beat them. let X = the number of times this player would win against 15 novice opponents.

Then the random variable x follows what type of distribution? (Select all that apply.)

a) Geometric
b) Binomial
c) Poisson

Answer 1

Binomial

Explanation:

No. of trials finite,

Success/failure

Answer 2

b) Binomial

c) Poisson

Explanation:

The geometric distribution is the number of trials required to have r successes. The measures the number of sucesses(wins), not the number of trials required to win r games. So the geometric distribution does not apply.

For each match, there are only two possible outcomes, either the skilled player wins, or he does not. The probability of the skilled player winning a game is independent of other games. So the binomial distribution applies.

We can also find the expected number of wins of the skilled player, which is 15*0.9 = 13.5. The Poisson distribution is a discrete distribution in which the only parameter is the expected number of sucesses. So the Poisson distribution applies.

So the correct answer is:

b) Binomial

c) Poisson